Comparing Data Sets –

Comparing data sets is one of the most frequently tested skills on GCSE Maths papers at both Foundation and Higher tier. AQA, Edexcel and OCR all require you to compare two distributions using an average and a measure of spread — and to write your comparisons in context. Many students lose marks not because they cannot calculate the statistics, but because they do not structure their comparison sentences correctly. This guide shows you exactly how to compare, what to write, and where students go wrong. For the full specification overview, see our complete GCSE Maths topics list.

What Does Comparing Data Sets Mean?

To compare two data sets, you need to make at least two statements:

1. A comparison of an average (mean, median or mode) — this tells you about the typical value.
2. A comparison of a measure of spread (range, interquartile range or standard deviation) — this tells you about consistency or variability.

Both statements must be in context — refer to what the data actually represents.

Key Formulas

Step-by-Step Method

1. Calculate or read off the relevant average for each data set (mean or median).
2. Calculate or read off the relevant measure of spread for each data set (range or IQR).
3. Compare the averages — state which is higher/lower and what this means in context.
4. Compare the spread — state which is larger/smaller and what this means in context (e.g. more consistent, more varied).
5. Use sentence starters such as "On average, Group A scored higher because their median is ..." and "Group B's results were more consistent because their IQR is smaller."

Worked Example 1 — Foundation Level

Question: Class A scored a mean of 62 marks and a range of 45 marks on a test. Class B scored a mean of 58 marks and a range of 30 marks. Compare the two classes.

Working:

Average: Class A has a higher mean (62 vs 58), so on average Class A scored higher on the test.

Spread: Class A has a larger range (45 vs 30), so Class A's marks were more spread out. Class B's marks were more consistent.

Answer: On average, Class A performed better because their mean is higher (62 compared to 58). However, Class B was more consistent because their range is smaller (30 compared to 45).

Worked Example 2 — Higher Level

Question: The box plots for two factories show: Factory X — median = 48 minutes, IQR = 14 minutes. Factory Y — median = 42 minutes, IQR = 22 minutes. Compare the time taken to complete a task at each factory.

Working:

Average: Factory X has a higher median (48 vs 42 minutes), meaning tasks typically take longer at Factory X.

Spread: Factory X has a smaller IQR (14 vs 22 minutes), meaning the completion times at Factory X are more consistent. Factory Y's times are more variable.

Answer: On average, Factory Y completes tasks more quickly because its median time is lower (42 vs 48 minutes). However, Factory X is more consistent in its completion times because its IQR is smaller (14 vs 22 minutes).

Worked Example 3 — Exam Style

Question: The heights (cm) of 10 sunflowers in Garden A are: 142, 148, 151, 155, 158, 160, 163, 167, 172, 180. Garden B has a median height of 165 cm and a range of 25 cm. Compare the two gardens.

Working:

Garden A: n = 10. Median = (5th + 6th) ÷ 2 = (158 + 160) ÷ 2 = 159 cm. Range = 180 − 142 = 38 cm.

Average: Garden B has a higher median height (165 cm vs 159 cm), so sunflowers in Garden B are typically taller.

Spread: Garden A has a larger range (38 cm vs 25 cm), so Garden A's heights are more spread out. Garden B's heights are more consistent.

Answer: On average, Garden B's sunflowers are taller (median 165 cm vs 159 cm). Garden A's sunflowers have more variation in height (range 38 cm vs 25 cm).

Common Mistakes

• Only comparing one measure. You must compare both an average AND a measure of spread to earn full marks.
• Not using context. Saying "Group A is higher" is not enough. Say "Group A scored higher on the test" or "Factory Y completed the task more quickly."
• Using different measures for each group. Compare like with like — use the median for both groups, not the mean for one and the median for the other.
• Confusing spread with average. A larger range does not mean a higher average — it means more variability.

Exam Tips

• If the question gives you box plots, use the median and IQR (not the mean and range).
• If the question gives you raw data, calculate the mean or median and the range or IQR for both data sets.
• Always make two separate, clearly labelled comparison points.
• Use linking words: "therefore", "which suggests", "meaning that".
• For box plot skills, see cumulative frequency and box plots. For averages, see mean, median, mode and range.

Practice Questions

Q1 (Foundation): Team A: mean = 3.2 goals per match, range = 6. Team B: mean = 2.8 goals per match, range = 3. Compare the two teams.

Q2 (Foundation): The mode of data set P is 15 and the mode of data set Q is 22. What does this comparison tell you?

Q3 (Higher): Box plot summary — Group X: median 72, IQR 18. Group Y: median 65, IQR 10. Compare the two groups in the context of exam marks.

Practise comparing data sets and more for free on GCSEMathsAI.

Related Topics

• Mean, Median, Mode and Range
• Cumulative Frequency and Box Plots
• Stem-and-Leaf Diagrams

Summary

Comparing data sets requires two statements: one comparing an average (mean or median) and one comparing a measure of spread (range or IQR). Both must be in context. Use the median and IQR when data is given in box plots; use the mean and range when given raw data or frequency tables. A higher average means the typical value is greater. A smaller spread means the data is more consistent. Structure your answer clearly with linking words and always refer to what the data represents.